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On the solutions of the $CP^{1}$ model in $(2+1)$ dimensions

A. M. Grundland·P. Winternitz·W. J. Zakrzewski
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Abstract

We use the methods of group theory to reduce the equations of motion of the $CP^{1}$ model in (2+1) dimensions to sets of two coupled ordinary differential equations. We decouple and solve many of these equations in terms of elementary functions, elliptic functions and Painlev{é} transcendents. Some of the reduced equations do not have the Painlev{é} property thus indicating that the model is not integrable, while it still posesses many properties of integrable systems (such as stable ``numerical'' solitons).

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A. M. Grundland, P. Winternitz, W. J. Zakrzewski. 1995-06-09. On the solutions of the $CP^{1}$ model in $(2+1)$ dimensions. https://doi.org/10.1063/1.531446

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